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M15-24

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M15-24 [#permalink]

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New post 16 Sep 2014, 00:56
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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

43% (01:00) correct 57% (01:16) wrong based on 108 sessions

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New post 16 Sep 2014, 00:56
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Official Solution:


Statement (1) by itself is insufficient. We do not know the scale of the triangle. If 0.001 is small compared to the sides of the triangle then \(AC\) almost equals \(AB + BC\) and thus angle \(ABC\) is obtuse. But if the sides are all small, 0.001 might not indicate that \(AC\) is about equal to \(AB + BC\).

Statement (2) by itself is sufficient. It means that \(\angle ABC = \angle BCA\). A triangle cannot have two angles that are both greater than 90 degrees.


Answer: B
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Re: M15-24 [#permalink]

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New post 03 Dec 2014, 02:38
it is good question :)

stmt1 : clearly insufficient.

Stmt2 is sufficient to answer , suppose there are three angle x,y, and z , so x+y+z=180 , x=y

so 2y+z=180, value will be maximum when 2y=z , so 2z=180 zmax=90 , it can be greater than 90 (sufficient)
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New post 07 Oct 2015, 10:26
Statement 2 :- If triangle ABC is isosceles right angle triangle at B ...then statement B is inavalid...for rest other triangle it is valid

some time yes and sometime no

So answer will be E here i guess

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New post 08 Oct 2015, 08:19
suyashtcs wrote:
Statement 2 :- If triangle ABC is isosceles right angle triangle at B ...then statement B is inavalid...for rest other triangle it is valid

some time yes and sometime no

So answer will be E here i guess


No, that's not correct. The second statement implies than angles B and C are equal and since a triangle cannot have two angles that are both greater than 90 degrees, then angle B must be less than 90 degrees.
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New post 08 Oct 2015, 08:36
thankyou for nice explanation :-) ....i was missing the key point...here

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Re: M15-24 [#permalink]

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New post 30 Jan 2017, 08:15
The answer must be option B.

First statement is just a re-statement of the in-equality theorem. Does not say anything about angle ABC.

Statement 2 on the other hand makes it clear that B can't be more than 90 if AC=AB. Hence the answer must be B.
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M15-24 [#permalink]

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New post 30 Aug 2017, 11:10
Bunuel wrote:
Official Solution:


Statement (1) by itself is insufficient. We do not know the scale of the triangle. If 0.001 is small compared to the sides of the triangle then \(AC\) almost equals \(AB + BC\) and thus angle \(ABC\) is obtuse. But if the sides are all small, 0.001 might not indicate that \(AC\) is about equal to \(AB + BC\).

Statement (2) by itself is sufficient. It means that \(\angle ABC = \angle BCA\). A triangle cannot have two angles that are both greater than 90 degrees.


Answer: B



Hi Bunuel Sir,

Can you please explain A option via any example.I am not able to comprehend the explanation.

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M15-24   [#permalink] 30 Aug 2017, 11:10
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